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risers), then draw h /, parallel to n m, which being the height of the frustum for the stairs; then from the centre x, describe the semicircle a b, whose diameter is eqnal to the diameter, a 5, fig. 1, or base of the frustum, also from the centre, 0, describe the semicircle, c e, whose diameter is equal to the diameter, c e, fig. 1, or expansion of the frustum; then set off the distance from a b and c e, equal to the length of the tread, a d, fig. 1; then draw the lines d / a c, b c, and h 4 which give the stairs its conical form.
To draw the concave string of fig. 2, and give it the spiral form.
Divide the semicircles a b and c e into half the number of parts there are treads in the given plan, fig. 1, and let fall perpendiculars from each point of division to the base of each of the semicircles, a b and c e, as is shown in the diagram at s t and u v; then from each of the points upon the base, a b, draw lines to each of the points in the base, c e, as from t to v, which gives the face of each riser upon the concave string; the convex string is formed in the same manner, thus far describing semicircles from d to k, and / to A, from the centres x and z, and dividing them into the same number of parts as a b and c e, and from each of the points of division, let fall perpendiculars to the base d k and fh; then from the point of division upon the base d k, draw lines to each of the points in the base / h, which gives the face of each riser upon the convex string; then from each of the parts upon the height rod, n A, draw lines parallel to the base, d k, which gives the line of each tread from the concave to the convex string; then from the upper edge of each riser upon the concave and convex strings, set down the depth of each string, and through those points trace out the curve or lower edge of the string. The elevation of the rail is traced out in the same manner which is supposed to be placed upon the balusters, that it may retain its proper height from the upper edge of the concave string.
To draw the plan of the railj as figs. 3 and 4, for the given plan, fig. 2.
Set up the height at a, fig. 2, equal to the height of the short baluster, as at d o; then draw o a to & parallel to the base d k at q, erect the perpendicular q c equal in